On strongly regular graphs with m2 = qm3 and m3 = qm2 for q = 7/2, 7/3, 7/4, 7/5, 7/6

Abstract

We say that a regular graph G of order n and degree r ≥ 1 (which is not the complete graph) is strongly regular if there exist non-negative integers τ and θ such that |Si ∩ Sj| = τ for any two adjacent vertices i and j, and |Si ∩ Sj| = θ for any two distinct non-adjacent vertices i and j, where Sk denotes the neighborhood of the vertex k. Let λ1 = r, λ2 and λ3 be the distinct eigenvalues of a connected strongly regular graph. Let m1 = 1, m2 and m3 denote the multiplicity of r, λ2 and λ3, respectively. We here describe the parameters n, r, τ and θ for strongly regular graphs with m2 = qm3 and m3 = qm2 for q = 7/2, 7/3, 7/4, 7/5, 7/6.